My primary research is in Partial Differential Equations (PDEs). We mainly study PDEs arising as models for waves on the water surface. Some famous examples of such PDEs are Korteweg de Vries (KdV), Benjamin-Bona-Mahony (BBM), Whitham, Boussinesq, Camassa-Holm, Kadomtsev-Petvishvili and Ostrovsky equations. We study stability of solutions of these PDEs.

My secondary research area is Machine Learning. We are interested in both application as well as theoretical aspects of machine learning. In application part, we use deep learning techniques to predict different characteristics of tropical cyclones. We are also exploring how numerical techniques involving PDEs modeling dynamics of tropical cyclones and deep learning techniques can be fused together to improve these predictions.

In theory, we analyze and improve upon current activation functions used in neural networks. We use several smoothing techniques to propose smoother version of well-known activation functions like ReLU and check their performance on variety of architectures and datasets.

I also work on some problems in number theory and game theory.